For the fabrication of current advanced semiconductor sevices, because of an increased number of I/O pins for improved performance and a reduction in package size, the conventional system of connecting semiconductor chips to lead frames using gold wires is employed less frequently. Under the circumstances, the flip chip system of mounting semiconductor chips to substrates or boards via solder is more frequently employed in the recent years. In the connecting method of this type, the reliability of semiconductor chips is improved by infiltrating a liquid epoxy resin into the space between semiconductor chips and substrates and curing the resin therein. Since the space between semiconductor chips and substrates is filled with the resin by capillary action, the filling step requires a very long time. If the viscosity of the resin composition is reduced in order to shorten the fill time, the inorganic filler in the encapsulating resin composition can settle during heat curing, resulting in a difference in expansion coefficient between upper and lower portions of the cured resin. This detracts from the reliability of semiconductor devices.